Hyperbolicity, heterodimensional cycles and Lyapunov exponents for partially hyperbolic dynamics

We prove a dichotomy of C² partially hyperbolic sets with one-dimensional center direction admitting no zero Lyapunov exponents, either hyperbolicity over the supports of ergodic measures or approximation by a heterodimensional cycle. This provides a partial result to the C¹ Palis Conjecture that claims a dichotomy, hyperbolicity or homoclinic bifurcations in a dense subset of the space of C¹ diffeomorphisms. Moreover, a theorem of Ma?é applied in the proof is modified to have an additional property concerning the Hausdorff distance between a periodic orbit and the support of a hyperbolic ergodic measure.     

Fabrication of high-efficiency diffraction gratings in glass

We investigated a microfabrication process for optical gratings with periods of micrometer order that use ultrafast laser pulses in semiconductor-doped glass. ZnS- or PbS-doped SiO2-A12O3-B2O3-CaO-ZnO-Na2O-K2O glass was prepared by a melting method. Glass transmission diffraction gratings with a high refractive-index difference were fabricated with femtosecond laser pulses. The first-order diffraction efficiencies of these gratings were approximately 80%, and the first-order diffraction angles of these gratings were 8 degrees at telecommunication wavelengths.     

Direct probe of the shape resonance mechanism in 2sigma(g)-shell photoionization of the N2 molecule

Angular distributions of photoelectrons from a 2sigma(g) shell of fixed-in-space N2 molecules have been measured for left- and right-elliptically polarized and for linearly polarized light at several photon energies in the region of sigma(*) shape resonance. That allowed the determination of a set of dipole matrix elements and phase shift differences characterizing the process. These data clearly show the enhancement of the fsigma(u) partial cross section in the resonance simultaneously with an abrupt increase of the corresponding phase shift by pi, which is the first experimental demonstration of the nature of the sigma(*) shape resonance in homonuclear diatomic molecules.     

Synthesis and evaluation of 1-arylsulfonyl-3-piperazinone derivatives as a factor Xa inhibitor II. Substituent effect on biological activities

Intravascular clot formation is an important event in a number of cardiovascular diseases. The prevention of blood coagulation has become a major target for new therapeutic agents. Factor Xa (FXa) is a trypsin-like serine protease that plays a key role in the blood coagulation cascade and represents an attractive target for anticoagulant drug development. We have investigated substituents in the central part of a lead compound (3: M55113), and discovered that compound M55551 (34: (R)-4-[(6-Chloro-2-naphthalenyl)sulfonyl]-6-oxo-1-[[1-(4-pyridinyl)-4-piperidinyl]methyl]-2-piperazinecarboxylic acid) is a potent inhibitor of FXa (IC(50)=0.006 microM), with high selectivity for FXa over trypsin and thrombin. The activity of this compound is ten times more powerful than the lead compound.     

Development of system and technology for m?ssbauer spectroscopic microscope

We have been developing a “M?ssbauer Spectroscopic Microscope (MSM)” which consists of a focusing lens for 14.4?keV γ-rays and a high precision X–Y stage. The measuring system both for electrons and γ-rays combined with a new M?ssbauer driver, i.e., “a moving coil actuator with a liner encoder” enables us to measure the mapping images simultaneously corresponding to different spectral components. The system has a controlling system based on a LabVIEW program and a LIST mode data acquisition system (NIKI-GLASS/A3100). To investigate a correlation between the microstructure of a sample and ⁵⁷Fe atoms, a scanning electron microscope (APCO/Mini-EOC) is also installed to this system.     

Synthesis of poly(Nε-phenoxycarbonyl-l-lysine) by polycondensation of activated urethane derivative and its application for selective modification of side chain with amines

We report a methodology for the synthesis of Nε-phenoxycarbonyl-protected poly(l -lysine) on the side chain by chain growth polycondensation of Nα,Nε-bis(phenoxycarbonyl)-l -lysine proceeded through the selective elimination of phenol and CO₂ from the Nα phenoxycarbonyl moiety at 50 °C in N,N-dimethylacetamide in the presence of a primary amine used as an initiator. After optimization of reaction condition, the addition of acetic acid during polycondensation proved effective for the realization of the predicted molecular weight and narrow dispersity of the corresponding polypeptide by adjusting the feed ratio of monomer to the amine initiator because of the suppression of interchain coupling that occurs between the amino terminus of poly(l -lysine) and the Nε-phenoxycarbonyl group on the polymer side chains. Furthermore, taking advantage of the potentially reactive Nε-phenoxycarbonyl moiety on the side chain, post-polymerization modification was effectively achieved by the nucleophilic reaction of amine compounds including primary, secondary, and aromatic amines through the formation of urea linkage, providing a useful platform for synthesis of selective side chain functionalization of poly(l -lysine) samples. © 2018 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2018 , 56, 2522–2530     

Synthesis and radical ring‐opening polymerization of vinylcyclopropanes derived from amino acids with hydrophobic moieties

Six 1,1‐disubstituted vinylcyclopropanes (VCP) were synthesized from glycine and amino acids bearing hydrophobic moieties, l ‐alanine, l ‐valine, l ‐leucine, l ‐isoleucine, and l ‐phenylalanine. These VCP derivatives efficiently underwent radical ring‐opening polymerization to afford the corresponding polymers bearing trans‐vinylene moiety in the main chains and the amino acid‐derived chiral moieties in the side chains. The polymers were film‐formable, and in the films of polymers bearing the glycine‐ and alanine‐derived side chains, presence of hydrogen bonding was confirmed by IR analysis. Thermogravimetric analysis of the polymers revealed that the temperatures of 5% weight loss were higher than 300 °C. Differential scanning calorimetry clarified that the polymers were amorphous ones showing glass transition temperatures in a range of 48–80 °C. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2017 , 55, 3996–4002     

Laurent biorthogonal polynomials, q-Narayana polynomials and domino tilings of the Aztec diamonds

A Toeplitz determinant whose entries are described by a q-analogue of the Narayana polynomials is evaluated by means of Laurent biorthogonal polynomials which allow of a combinatorial interpretation in terms of Schröder paths. As an application, a new proof is given to the Aztec diamond theorem by Elkies, Kuperberg, Larsen and Propp concerning domino tilings of the Aztec diamonds. The proof is based on the correspondence with non-intersecting Schröder paths developed by Johansson.